CAT 2022 Slot 1 QA Q20 Ratio, Mixtures & Averages

Question 20 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
  1. A
    1 : 2
  2. B
    3 : 1
  3. C
    1 : 4
  4. D
    4 : 1

Answer: (D) 4 : 1 Ratio, Mixtures & Averages MCQ

Solution

  1. Let \(n\) original students with average \(A\), \(m\) new with average \(A + 3\).
  2. New average \(= A + \frac{3m}{n + m} = A + 0.6\), so \(\frac{m}{n + m} = \frac{1}{5}\).
  3. \(n : m = 4 : 1\).

Shortcut. Alligation: 0.6 and 2.4 are the distances, so the ratio is \(2.4 : 0.6 = 4 : 1\).

Same concept in other years

See every question on Average changes when members join or leave the group.

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